Details

Time bar (total: 32.1s)

sample62.0ms

Algorithm
intervals
Results
27.0ms60×body1280valid
14.0ms56×body640valid
6.0ms22×body2560valid
4.0ms28×body320valid
2.0ms75×body80valid
1.0ms15×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0105
1105

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 49.7b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

1.2b
(+ x (sqrt (+ (* x x) 1.0)))
2.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
12.3b
(sqrt (+ (* x x) 1.0))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×*-un-lft-identity
6×add-cube-cbrt
5×pow1 sqrt-prod hypot-def add-log-exp
4×add-exp-log log-prod distribute-lft-out
3×expm1-log1p-u fma-def flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
2×log-div sqrt-div
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 swap-sqr rem-log-exp associate-*l* sum-log log-pow *-commutative unswap-sqr
Counts
3 → 58
Calls
3 calls:
11.0ms
(+ x (sqrt (+ (* x x) 1.0)))
11.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
10.0ms
(sqrt (+ (* x x) 1.0))

series291.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(+ x (sqrt (+ (* x x) 1.0)))
179.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
50.0ms
(sqrt (+ (* x x) 1.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0331431
11121393
25002372

prune192.0ms

Filtered
67 candidates to 57 candidates (85.1%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New64367
Fresh000
Picked101
Done000
Total65368

Merged error: 0b

Counts
68 → 3

localize12.0ms

Local error

Found 1 expressions with local error:

0.3b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
189×add-sqr-sqrt
149×unpow-prod-down cube-prod
126×*-un-lft-identity
125×add-cube-cbrt
86×sqrt-prod
42×sqr-pow
33×associate-*r/
32×cube-mult unpow3
25×unswap-sqr
24×add-exp-log
18×associate-/r*
13×associate-/l*
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×clear-num un-div-inv cbrt-unprod
1×cbrt-undiv expm1-log1p-u frac-2neg pow-prod-down *-commutative log1p-expm1-u div-inv add-log-exp
Counts
1 → 306
Calls
1 calls:
66.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series335.0ms

Counts
1 → 3
Calls
1 calls:
334.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify109.0ms

Algorithm
egg-herbie
Counts
309 → 309
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
07801893
142491476
250011476

prune422.0ms

Filtered
309 candidates to 114 candidates (36.9%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New3090309
Fresh022
Picked011
Done000
Total3093312

Merged error: 0b

Counts
312 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

1.2b
(+ x (hypot x (sqrt 1.0)))
2.8b
(log (+ x (hypot x (sqrt 1.0))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
4×add-sqr-sqrt add-cube-cbrt log-prod add-log-exp
3×pow1 add-exp-log fma-def
2×expm1-log1p-u log-div flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
1×+-commutative rem-log-exp sum-log log-pow
Counts
2 → 34
Calls
2 calls:
3.0ms
(+ x (hypot x (sqrt 1.0)))
3.0ms
(log (+ x (hypot x (sqrt 1.0))))

series413.0ms

Counts
2 → 6
Calls
2 calls:
126.0ms
(+ x (hypot x (sqrt 1.0)))
286.0ms
(log (+ x (hypot x (sqrt 1.0))))

simplify79.0ms

Algorithm
egg-herbie
Counts
40 → 40
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
0238284
1786255
23259247
35001245

prune99.0ms

Filtered
40 candidates to 33 candidates (82.5%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New40040
Fresh011
Picked011
Done011
Total40343

Merged error: 0b

Counts
43 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0.0625) (pow x 5))
0.5b
(/ 0.125 (pow x 3))
12.6b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
17.8b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
13032×frac-sub
8815×associate-/r*
7012×add-sqr-sqrt
6505×associate-/l*
6460×*-un-lft-identity
6026×add-cube-cbrt
3278×log-div
2802×times-frac
2716×unpow-prod-down
1522×prod-diff
1410×frac-2neg clear-num
1311×distribute-rgt-neg-in
1269×distribute-lft-neg-in
1241×cube-prod
965×associate--r+
960×sqr-pow
423×neg-mul-1
413×cube-mult unpow3
330×difference-of-squares
134×distribute-lft-out--
104×div-inv
40×fma-neg
38×flip3-- flip--
15×add-exp-log
12×log-prod
9×add-log-exp
8×add-cbrt-cube
6×div-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×diff-log
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg div-sub pow-exp associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 8339
Calls
4 calls:
7.0ms
(/ (- 0.0625) (pow x 5))
13.0ms
(/ 0.125 (pow x 3))
474.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
335.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series340.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (- 0.0625) (pow x 5))
35.0ms
(/ 0.125 (pow x 3))
190.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
63.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify2.5s

Algorithm
egg-herbie
Counts
8351 → 8351
Iterations

Useful iterations: 0 (110.0ms)

IterNodesCost
013127244273

prune23.1s

Filtered
8351 candidates to 4897 candidates (58.6%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New835108351
Fresh000
Picked011
Done022
Total835138354

Merged error: 0b

Counts
8354 → 3

regimes22.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.5b

bsearch75.0ms

Steps
ItersRangePoint
8
2.0262054515877825e-05
0.3235305135594418
0.0010048358779444152
10
-85019.06990604498
-4.503960361653909e-11
-1.0167321160990819

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03924
13924

end0.0ms

sample1.8s

Algorithm
intervals
Results
937.0ms2346×body1280valid
347.0ms1551×body640valid
204.0ms802×body2560valid
99.0ms770×body320valid
64.0ms2096×body80valid
32.0ms435×body160valid